Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
7646 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 2232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C24×#170 | C2 | semidirect |
| 3. C22×C22⋊#170 | C2 | direct (N × H) |
| 11. C23×#170 | C22 | semidirect |
| 12. C2×C22⋊#170 | C22 | direct (N × H) |
| 16. C25×C5 | C8 | semidirect |
| 29. C22×#170 | C23 | semidirect |
| 30. C22⋊#170 | C23 | direct (N × H) |
| 39. C24×C5 | C2×C8 | semidirect |
| 54. C2×#170 | C24 | semidirect |
| 67. C23×C5 | C22⋊C8 | semidirect |
| 70. C23×C5 | C22×C8 | semidirect |
| 85. C25 | #170 | semidirect |
| 103. C22×C5 | C2×C22⋊C8 | semidirect |
| 106. C22×C5 | C23×C8 | semidirect |
| 116. C24 | C2×#170 | semidirect |
| 134. C2×C5 | C22×C22⋊C8 | semidirect |
| 141. C23 | C22⋊#170 | direct (N × H) |
| 143. C23 | C22×#170 | semidirect |
| 157. C5 | C23×C22⋊C8 | semidirect |
| 161. C22 | C2×C22⋊#170 | direct (N × H) |
| 163. C22 | C23×#170 | semidirect |
| 171. C2 | C22×C22⋊#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic5 | 2 |
| C24×#170 | 2 |
| C22×C22⋊#170 | 2 |
| C23×C22⋊C8 | 5 |